The current study aimed to develop a meshfree Lagrangian particle method for the Landau-Lifshitz Navier-Stokes (LLNS) equations. The LLNS equations incorporate thermal fluctuation into macroscopic hydrodynamics by addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation theorem. Moreover, the study focuses on capturing correct variance and correlation computed at equilibrium flows, which are compared with available theoretical values and found very good agreement
